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We extend the existing framework of semiimplicit variational inference (SIVI) and introduce doubly semi-implicit variational inference (DSIVI), a way to perform variational inference and learning when both the approximate posterior and the prior distribution are semi-implicit. In other words, DSIVI performs inference in models where the prior and the posterior can be expressed as an intractable infinite mixture of some analytic density with a highly flexible implicit mixing distribution. We provide a sandwich bound on the evidence lower bound (ELBO) objective that can be made arbitrarily tight. Unlike discriminator-based and kernel-based approaches to implicit variational inference, DSIVI optimizes a proper lower bound on ELBO that is asymptotically exact. We evaluate DSIVI on a set of problems that benefit from implicit priors. In particular, we show that DSIVI gives rise to a simple modification of VampPrior, the current state-of-theart prior for variational autoencoders, which improves its performance.

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The article considers the main models incorporated in the developed software package for modeling reliability indicators of nuclear reactor unit (RF) complex technical systems by the Monte Carlo method. Approaches to organization of system state determination on the layout basis into groups, principles of accounting for dependent failures and incomplete recovery are described. Two distribution laws are provided as ones for a random time distribution to failure of the modeled system single element. Relations are given for the generation of random time to failure when using these distributions. Since the most of reactor safety systems operate in standby mode, a separate consideration is given to the organization of systems operating simulations in standby mode. It is important that the elements of such systems are periodically tested, and this periodicity can be different for different elements of the one system. Tests / testing availability of safety systems significantly affects the evaluation of their performance indicators. Therefore, the developed program complex takes into account the tests availability and their different frequency for individual elements of one system. The implementation description of accounting for periodic testing in the framework of reliability modeling is also given in this paper. The various types' features of recovery are considered, in terms of their account at modeling. So, for example, instant recovery of some elements of the system and random for others, are possible. A specific attention is paid to the principles of accounting for different types of recovery in the modeling, together with the influence of dependent failures. Estimates of reliability indicators depend significantly on the types of recovery, and if the different nature of the recovery time and the time of its start is not taken into account, there may be a significant distortion of the modeling results. Incomplete recovery's estimation is made on a base of the relatively simple heuristic model described in this paper. The use of the proposed incomplete recovery model is provided for modeling the reliability of the system. The operation principle of the developed calculation code for modeling the reliability of NPP complex technical systems is precisely described, taking into account all the specified features.